Dear Dr. Linder; I think what are you trying to say is that:  how the defect structure of XY2O4 spinel (normal or inverse) will change if one creates  oxygen deficiency in the structure by exposing reducing atmosphere such as H2/N2  keeping the charge neutrality.  In order to answer to this question we have to know the charge states of  X  and Y  cations. As you may know there are three types:  X2+ Y3+ ; X4+ Y2+ ;  ; X6+ Y+.

Symbolically  for the first case we can write:  

  [ XY2O4]   +  H2=   H2O   +  V2-X  + V2+O +  X   + {XY2O4}   X  has tetrahedral coordination

 [XY2O4] + 3H2= 3H2O + 2V3-Y +3 V2+O + 2 Y + {XY2O4} Y  has octahedral coordination

Where  VX  and  VY  are cation vacancies created to compensate the oxygen anion deficiency due to redox reaction.  {.]  indicates defected spinel structures. These two hypothetical  defect reactions may take place  simultaneously or individual with different proportion depending upon the affinities of the cations and anions defects. Here we created Schottky  defect pairs. 

Cation vacancies have positive effective charge and Anion vacancies have negative effective charge.  Electrical conduction is ionic and conductivity closely related to the diffusivities through the Einstein-Nerst relationship.

If one looks at the structure of spinel there 32 O in the unit cell, which is almost cubic and closed packed (Wells, 1962). There are 64 tetrahedral sites and 32 octahedral sites, and  8X occupy tetrahedral sites and 16Y occupy octahedral sites. My expectation is the  atomic mobility  of  X cations, which is tetrahedrally coordinated by 4O  controls the ionic conductivity if the vacancy exchange mechanism is operating due to the fact that there are abundance number of  tetrahedral sites are available in the lattice. BUT of course one has the worry activation free energy  barrier  delG* for the atomic jump  probability of X species from one tetrahedral site to another neighboring tetrahedral site, which is a critical rate determining factor due to the exponential   NVX exp[-delG*/RT] dependence on it. 

Hi Markus,

The decomposition of the spinel results in a change in crystal chemistry by increasing the number and types of defects present. This in turn can effect both grain boundary mobility and electrical conductivity. I have attached two papers that might help.  

Regards,

Keith

http://onlinelibrary.wiley.com/doi/10.1111/j.1151-2916.1989.tb06113.x/abstract

http://onlinelibrary.wiley.com/doi/10.1111/j.1151-2916.1990.tb05172.x/abstract

Dear Dr. Linder; I think what are you trying to say is that:  how the defect structure of XY2O4 spinel (normal or inverse) will change if one creates  oxygen deficiency in the structure by exposing reducing atmosphere such as H2/N2  keeping the charge neutrality.  In order to answer to this question we have to know the charge states of  X  and Y  cations. As you may know there are three types:  X2+ Y3+ ; X4+ Y2+ ;  ; X6+ Y+.

Symbolically  for the first case we can write:  

  [ XY2O4]   +  H2=   H2O   +  V2-X  + V2+O +  X   + {XY2O4}   X  has tetrahedral coordination

 [XY2O4] + 3H2= 3H2O + 2V3-Y +3 V2+O + 2 Y + {XY2O4} Y  has octahedral coordination

Where  VX  and  VY  are cation vacancies created to compensate the oxygen anion deficiency due to redox reaction.  {.]  indicates defected spinel structures. These two hypothetical  defect reactions may take place  simultaneously or individual with different proportion depending upon the affinities of the cations and anions defects. Here we created Schottky  defect pairs. 

Cation vacancies have positive effective charge and Anion vacancies have negative effective charge.  Electrical conduction is ionic and conductivity closely related to the diffusivities through the Einstein-Nerst relationship.

If one looks at the structure of spinel there 32 O in the unit cell, which is almost cubic and closed packed (Wells, 1962). There are 64 tetrahedral sites and 32 octahedral sites, and  8X occupy tetrahedral sites and 16Y occupy octahedral sites. My expectation is the  atomic mobility  of  X cations, which is tetrahedrally coordinated by 4O  controls the ionic conductivity if the vacancy exchange mechanism is operating due to the fact that there are abundance number of  tetrahedral sites are available in the lattice. BUT of course one has the worry activation free energy  barrier  delG* for the atomic jump  probability of X species from one tetrahedral site to another neighboring tetrahedral site, which is a critical rate determining factor due to the exponential   NVX exp[-delG*/RT] dependence on it. 

Thanks a lot for your quick response, which is already useful for the understanding.

In our experiment we observed a total decomposition of the spinel (XY2O4) phase. These is confirmed by XRD patterns i.e. no remaining spinel phase could be proved after 12 h in forming gas atmosphere at 850 °C. I assume that the observed electrical conductivity is related to a metallic matrix of X, since the electrical conductivity was further increased during temperature decrease.

Hence I assume defect/decomposition can proceed according to

XY2O4 + H2 = V2-X + V2+O + Y2O3 + X(g) + H2O

Oxygen vacancies may form some pores and X(g) agglomerates to X(s). Thereby dispersion of the metallic X(s) leads to percolating path preferred by the electrical current. Consequently the electrical conductivity and the defect structure, respectively of the Y2O3 phase can be neglected in respect to the overall electrical conductivity.

I’m looking forward to some comments and hints to this hypothesis. Thank you.

Markus

Dear Marcus, your theory looks  very plausible.  In order to make sound decision about the reaction  we have to determine   (by any other available means) the chemical content of the reaction  products .   The negative temperature variation of conductivity indicates that you may have metallic conduction. This a affirmative  clue for your hypothesis.

 Y2O3  there are three structures found in the nature (Wells, 1962)  alpha-corundum, the so called  A and C  rare -earth sesquioxide structures.  I have no idea about your chemical species. But if your case would be  alpha-corundum life would be easy for me to speculate wisely!  Since corundum has closed packed cubic structure, where metal atoms occupy octahedral sites surrounded by six oxygen atoms, and each oxygen atoms is surrounded by four  metal ions. After seen the packing of corundum structure, which is based on the  closed packed  oxygen atoms having six fold rotational symmetry. The available interstices sites for Y is one-half of the oxygen atoms, therefore  it is not possible to have layer structure for  Y2O3 unless one has cation  deficiency such as

Y2O3 + H2= {Y3+2 O32-. + V2+O+H2 O  +2e-}.   and   X2+ + 2 e- = X  (precipitates) 

You may have also Frenkel defect pair such as: [{V2-O  ; X2+}. but this is  not the case according to Marcus observation of metallic conductivity.

you can simply use pyrolsis technique,